A system includes a device, a support structure, and a flexure bearing configured to connect the device to the support structure. The flexure bearing includes an outer hub and an inner hub, where the hubs are configured to be secured to the support structure and to the device. The flexure bearing also includes multiple sets of flexure arms connecting the outer and inner hubs. Each set of flexure arms includes symmetric flexure arms. The flexure bearing could include three sets of flexure arms positioned radially around a central axis of the flexure bearing and having a spacing of about 120°. Each flexure arm can follow a substantially curved path between the outer hub and the inner hub. The symmetric flexure arms in each set can be configured such that twisting of one flexure arm in one set is substantially counteracted by twisting of another flexure arm in that set.